Motivated by aspects of robustness in parsing a context-free language, we study generalized fuzzy context-free grammars. These fuzzy context-free $K$-grammars provide a general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. They model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Formally, a fuzzy context-free $K$-grammar is a fuzzy context-free grammar with a countable rather than a finite number of rules satisfying the following condition: for each symbol $\alpha$, the set containing all right-hand sides of rules with left-hand side equal to $\alpha$ forms a fuzzy language that belongs to a given family $K$ of fuzzy languages. We investigate the generating power of fuzzy context-free $K$-grammars, and we show that under minor assumptions on the parameter $K$, the family of languages generated by fuzzy context-free $K$-grammars possesses closure properties very similar to those of the family of ordinary context-free languages.
展开▼
机译：基于解析上下文无关语言的鲁棒性，我们研究了广义模糊上下文无关文法。这些模糊的无上下文上下文$ K $语法提供了一个通用框架，可以通过单个生成机制正确描述以及错误地导出句子。他们模拟了在每个无上下文派生步骤中从可能的语法错误中做出无限选择的情况。形式上，模糊上下文无关的$ K $语法是一种模糊上下文无关的语法，具有可计数而不是有限数量的规则，它们满足以下条件：对于每个符号$ \ alpha $，包含所有右侧的集合的左手边等于$ \ alpha $的规则的组合形成一种模糊语言，该模糊语言属于给定的族$ K $模糊语言。我们研究了模糊上下文无关的$ K $语法的生成能力，并且表明在参数$ K $的较小假设下，模糊上下文无关的$ K $语法生成的语言族具有非常相似的闭包特性与普通的无上下文语言族相对应。
展开▼
